{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "from scipy.stats import poisson\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "MAX_CARS = 20\n",
    "MOVING_COST_OF_CAR = 2\n",
    "RENTAL_GET_OF_CAR = 10\n",
    "RENTAL_REQUEST_OF_FIRST_LOCATION = 3\n",
    "RENTAL_REQUEST_OF_SECOND_LOCATION = 4\n",
    "RETURN_NUM_OF_FIRST_LOCATION = 3\n",
    "RETURN_NUM_OF_SECOND_LOCATION = 2\n",
    "DISCOUNT = 0.9\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "poisson_cache = dict()\n",
    "POISSON_UPPER_BOUND = 10\n",
    "def poisson_prob(k, lam):\n",
    "    global poisson_cache\n",
    "    key = k * 10 + lam\n",
    "    if key not in poisson_cache:\n",
    "        poisson_cache[key] = poisson.pmf(k, lam)\n",
    "    return poisson_cache[key]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def expected_return(state, action, state_value, constanted_return_car=True):\n",
    "    returns = 0.0\n",
    "    returns -= abs(action) * MOVING_COST_OF_CAR\n",
    "    # current car\n",
    "    NUM_OF_CAR_FIRST_LOC = min(state[0] - action, MAX_CARS)\n",
    "    NUM_OF_CAR_SECOND_LOC = min(state[1] + action, MAX_CARS)\n",
    "    \n",
    "    for rental_num_of_car_first_loc in range(POISSON_UPPER_BOUND):\n",
    "        for rental_num_of_car_second_loc in range(POISSON_UPPER_BOUND):\n",
    "            prob = poisson_prob(rental_num_of_car_first_loc, RENTAL_REQUEST_OF_FIRST_LOCATION) * \\\n",
    "                poisson_prob(rental_num_of_car_second_loc, RENTAL_REQUEST_OF_SECOND_LOCATION)\n",
    "            num_of_car_first_loc = NUM_OF_CAR_FIRST_LOC\n",
    "            num_of_car_second_loc = NUM_OF_CAR_SECOND_LOC\n",
    "            valid_rental_first_loc = min(NUM_OF_CAR_FIRST_LOC, rental_num_of_car_first_loc)\n",
    "            valid_rental_second_loc = min(NUM_OF_CAR_SECOND_LOC, rental_num_of_car_second_loc)\n",
    "            rewards = (valid_rental_first_loc + valid_rental_second_loc) * RENTAL_GET_OF_CAR\n",
    "            num_of_car_first_loc -= valid_rental_first_loc\n",
    "            num_of_car_second_loc -= valid_rental_second_loc\n",
    "            \n",
    "            if constanted_return_car:\n",
    "                return_car_first_loc = RETURN_NUM_OF_FIRST_LOCATION\n",
    "                return_car_second_loc = RETURN_NUM_OF_SECOND_LOCATION\n",
    "                num_of_car_first_loc = min(num_of_car_first_loc + return_car_first_loc, MAX_CARS)\n",
    "                num_of_car_second_loc = min(num_of_car_second_loc + return_car_second_loc, MAX_CARS)\n",
    "                returns += prob * (rewards + DISCOUNT * state_value[num_of_car_first_loc, num_of_car_second_loc])\n",
    "            else:\n",
    "                for return_car_first_loc in range(POISSON_UPPER_BOUND):\n",
    "                    for return_car_second_loc in range(POISSON_UPPER_BOUND):\n",
    "                        prob_return = poisson_prob(return_car_first_loc, RETURN_NUM_OF_FIRST_LOCATION) * \\\n",
    "                                poisson_prob(return_car_second_loc, RETURN_NUM_OF_SECOND_LOCATION)\n",
    "                        num_of_car_first_loc_ = min(num_of_car_first_loc + return_car_first_loc, MAX_CARS)\n",
    "                        num_of_car_second_loc_ = min(num_of_car_second_loc + return_car_second_loc, MAX_CARS)\n",
    "                        returns += prob * prob_return * (rewards + DISCOUNT * state_value[num_of_car_first_loc_, num_of_car_second_loc_])\n",
    "\n",
    "    return returns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
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",
      "text/plain": [
       "<Figure size 4000x2000 with 12 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# maximum # of cars to move during night\n",
    "MAX_MOVE_OF_CARS = 5\n",
    "# all possible actions\n",
    "actions = np.arange(-MAX_MOVE_OF_CARS, MAX_MOVE_OF_CARS + 1)\n",
    "\n",
    "def figure_4_2(constant_returned_cars=True):\n",
    "    value = np.zeros((MAX_CARS + 1, MAX_CARS + 1))\n",
    "    policy = np.zeros(value.shape, dtype=np.int32)\n",
    "\n",
    "    iterations = 0\n",
    "    _, axes = plt.subplots(2, 3, figsize=(40, 20))\n",
    "    plt.subplots_adjust(wspace=0.1, hspace=0.2)\n",
    "    axes = axes.flatten()\n",
    "    while True:\n",
    "        fig = sns.heatmap(np.flipud(policy), cmap=\"YlGnBu\", ax=axes[iterations])\n",
    "        fig.set_ylabel('# cars at first location', fontsize=30)\n",
    "        fig.set_yticks(list(reversed(range(MAX_CARS + 1))))\n",
    "        fig.set_xlabel('# cars at second location', fontsize=30)\n",
    "        fig.set_title('policy {}'.format(iterations), fontsize=30)\n",
    "\n",
    "        # policy evaluation (in-place)\n",
    "        while True:\n",
    "            old_value = value.copy()\n",
    "            for i in range(MAX_CARS + 1):\n",
    "                for j in range(MAX_CARS + 1):\n",
    "                    new_state_value = expected_return([i, j], policy[i, j], value, constanted_return_car=constant_returned_cars)\n",
    "                    value[i, j] = new_state_value\n",
    "            max_value_change = abs(old_value - value).max()\n",
    "            print('max value change {}'.format(max_value_change))\n",
    "            if max_value_change < 1e-4:\n",
    "                break\n",
    "        # policy improvement\n",
    "        policy_stable = True\n",
    "        for i in range(MAX_CARS + 1):\n",
    "            for j in range(MAX_CARS + 1):\n",
    "                old_action = policy[i, j]\n",
    "                actions_returns = []\n",
    "                for action in actions:\n",
    "                    if -j <= action <= i:\n",
    "                        actions_returns.append(expected_return([i, j], action, value, constanted_return_car=constant_returned_cars))\n",
    "                    else:\n",
    "                        actions_returns.append(-np.inf)\n",
    "                new_action = actions[np.argmax(actions_returns)]\n",
    "                policy[i, j] = new_action\n",
    "                if policy_stable and old_action != new_action:\n",
    "                    policy_stable = False\n",
    "        print('policy stable {}'.format(policy_stable))\n",
    "        if policy_stable:\n",
    "            fig = sns.heatmap(np.flipud(value), cmap=\"YlGnBu\", ax=axes[-1])\n",
    "            fig.set_ylabel('# cars at first location', fontsize=30)\n",
    "            fig.set_yticks(list(reversed(range(MAX_CARS + 1))))\n",
    "            fig.set_xlabel('# cars at second location', fontsize=30)\n",
    "            fig.set_title('optimal value', fontsize=30)\n",
    "            break\n",
    "\n",
    "        iterations += 1\n",
    "figure_4_2()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "rl",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.20"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
